Question: Subtract $5y^2-6y-11$ from $6y^2+2y+5$.
Explanation: Since we are asked to subtract $5y^2-6y-11$ from $6y^2+2y+5$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $7$ from $1$ ", we would rewrite it as $1 - 7$. In other words, we would start with $1$ and then subtract $7$. Let's use this pattern to rewrite the problem as one expression: ${(6y^2+2y+5)-(5y^2-6y-11)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(6y^2+2y+5){-}(5y^2-6y-11)\\ \\ =&(6y^2+2y+5){-}5y^2{-}(-6y){-}(-11)\\ \\ =&6y^2+2y+5-5y^2+6y+11 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${y^2}, {y},$ and the $\text{{constant}}$ term: ${{6y^2} {+2y} {+5} {-5y^2} {+6y} {+11}}$ Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(6-5)y^2} + {(2+6)y} + {(5+11)}}$ When we combine the coefficients in front of each term, we get the following trinomial: ${y^2+8y+16}$